Wavelet Transform

# Wavelet Transform - Wavelet Transform A very brief look...

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Wavelet Transform A very brief look

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2 Wavelets vs. Fourier Transform In Fourier transform (FT) we represent a signal in terms of sinusoids FT provides a signal which is localized only in the frequency domain It does not give any information of the signal in the time domain
3 Wavelets vs. Fourier Transform Basis functions of the wavelet transform (WT) are small waves located in different times They are obtained using scaling and translation of a scaling function and wavelet function Therefore, the WT is localized in both time and frequency

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4 Wavelets vs. Fourier Transform In addition, the WT provides a multiresolution system Multiresolution is useful in several applications For instance, image communications and image data base are such applications
5 Wavelets vs. Fourier Transform If a signal has a discontinuity, FT produces many coefficients with large magnitude ( significant coefficients) But WT generates a few significant coefficients around the discontinuity Nonlinear approximation is a method to benchmark the approximation power of a transform

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6 Wavelets vs. Fourier Transform In nonlinear approximation we keep only a few significant coefficients of a signal and set the rest to zero Then we reconstruct the signal using the significant coefficients WT produces a few significant coefficients for the signals with discontinuities Thus, we obtain better results for WT nonlinear approximation when compared with the FT
7 Wavelets vs. Fourier Transform

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## Wavelet Transform - Wavelet Transform A very brief look...

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